Liverpool expect to complete the £15m signing of Joe Allen "in the next 24 hours", according to their manager, Brendan Rodgers, having eased into the Europa League play-offs against FC Gomel.

The Swansea City midfielder was at Anfield to witness Fabio Borini, Steven Gerrard and Glen Johnson score in the third qualifying round defeat of the Belarusians. Allen had earlier told Swansea he wished to be reunited with his former manager Rodgers at Anfield and is scheduled to undergo a medical on Friday after Liverpool met the release clause in his contract.

"It is obviously imminent," the Liverpool manager said. "He's here and that means there has been good communication with Swansea. We hope to conclude it within the next 24 hours, and that's as much as I can say." Daniel Agger and Andy Carroll, two Liverpool players who could be sold to increase Rodgers' transfer budget, received raucous receptions from the Kop throughout. "There is nothing new to add on Daniel," said Rodgers, with Manchester City having had a £20m offer for the Denmark international rejected. "He is very important to me. I like to have a playmaker from behind and I don't want to sell him."

There was marked improvement on Liverpool's first-leg performance that was not exclusively down to an extra week's training. Luis Suárez was unavailable in Belarus. He was unplayable at Anfield. From the back, where José Reina played short passes under pressure, there were clear signs of Rodgers' ideas taking hold. There was an urgency in the final third, a demand for one- and two-touch passing in and around the opposition penalty area and, with Borini linking well with Suárez, Gomel were bystanders.

Suárez created two first-half goals and tormented Gomel defenders in the process. Having collected a pass from Lucas Leiva, whose return from a cruciate ligament injury will be invaluable to Rodgers, the striker left Igor Kuzmenok for dead on the byline. His low cross was blocked by Nikolai Kashevski but only as far as Borini, who volleyed cleanly inside the near post.

Gerrard's 39th European goal arrived when Suárez glided beyond two defenders, drew the goalkeeper and squared for his captain to convert into an empty net. Gerrard also struck a post before Johnson provided the coup de grace with an emphatic half-volley into the top corner of Vladimir Bushma's goal from over 20 yards.